【作者】 王炜；

【导师】 牛凯；

【作者基本信息】 北京邮电大学 ， 信息与通信工程， 2025， 博士

【摘要】 极化码是由Arkan教授提出的一种被严格数学证明可达香农极限的编码方法,其核心在于信道极化理论。极化码凭借有限码长下的优异纠错性能,被5GNR标准采纳为增强移动带宽场景控制信道的编码方案,具有实用与研究的价值。尽管极化码在5G中己实现商用,其在未来通信系统(如6G)中的扩展仍面临多重挑战。信道极化思想不仅是编码领域的革命性突破,同时还揭示了通信系统中广泛存在的数据流传输可靠性差异都可以被视为一种广义极化现象。以理论性能分析为指导的极化编码与信号传输技术的联合优化,仍有较大的研究空缺。有鉴于此,本文从无线通信系统普遍存在的广义极化现象入手,对极化编码理论进行研究,提出矩阵扩展框架。然后在矩阵扩展框架基础上,将极化编码和信道传输技术进行联合设计,提出了基于矩阵扩展的极化编码传输理论与方法。从而为极化码在下一代移动通信系统中的应用提供有力的理论和方法支撑。具体来看,本文包括以下三个方面的创新工作:第一,对高阶调制下的极化编码HARQ进行了研究与设计。基于信道极化编码设计思想对HARQ与编码调制两类问题进行深入研究,提出了一种矩阵扩展(ME)方案,作为研究在比特交织极化编码调制(BIPCM)下的极化编码HARQ的框架。BIPCM中的ME方案能够将多个独立的极化子码通过矩阵扩展作用,组合形成更长的极化码,并且每个极化子码的长度可以是任意值。ME-BIPCM方案可以分为三个步骤:极化子码、矩阵扩展和调制极化。HARQ中的ME方案可以在ME-BIPCM方案的基础上进一步进行矩阵扩展,可以将多次传输的ME-BIPCM方案组合在一起,形成更长的极化码。ME-HARQ方案可以分为四个步骤:极化子码、矩阵扩展(调制子码块)、矩阵扩展(传输码块)和调制极化。当底层信道不一致时,例如高阶调制的极化效应会导致信道可靠性不一致,固定序列(如5G标准中极化序列或极化重量(PW)序列)不适用于极化码构造。ME方案通过按照底层信道的可靠性划分不同的块,使得每个极化子码上的底层信道可靠度是均匀的。基于ME方案的这一特性,本文还提出了一种码率分配(RA)方法,以研究ME方案的快速构造。在码块长趋于无穷时,基于RA构造的ME方案可被证明是能够达到信道容量的。仿真结果表明,相较于GA构造,基于RA构造的ME方案能够在复杂度大幅降低的同时,获得几乎相同的性能,并且在不同参数条件下表现出较强的鲁棒性。同时,相比较5G标准中的LDPC编码调制方案,可以获得稳定的性能增益。第二,对信源-信道联合极化编码理论进行研究,提出了一种基于矩阵扩展(ME)的信源-信道联合编码(JSCC)方案。ME-JSCC方案在矩阵扩展框架的基础上将信源极化编码(SPC)和信道极化编码进行了联合设计。信源极化编码可以分为无损SPC和有损SPC,并根据无损SPC和有损SPC设计了采用无损SPC的ME-JSCC方案和采用有损SPC的ME-JSCC方案。当信道条件好的时候应采取无损SPC。而信道条件差的时候,接收端很难实现无失真信源的恢复,此时应该采取有损SPC。ME-JSCC方案利用到极化编码矩阵是一个下三角矩阵,通过扩展极化编码矩阵可以形成更大的联合极化编码矩阵,从而得到更长的极化码。ME-JSCC方案能够增强信源与信道之间的耦合,从而实现更强的信源-信道联合极化效应。仿真结果表明,采用无损SPC的ME-JSCC方案优于DP-LDPC方案和基于J-SCL译码器下的双极化码方案,并且在短码长条件下可接近无损JSCC有限码长理论性能界。在低信噪比条件下,所提出的采用有损SPC的ME-JSCC方案相比于采用无损SPC的ME-JSCC方案能够获得进一步的性能提升。此外,基于自适应有损信源压缩率方法获得的压缩率与基于穷举搜索获得的最优压缩率条件下采用有损SPC的ME-JSCC方案的性能几乎一致,从而验证了所提出的自适应有损信源压缩率方法的有效性。第三,为了进一步提高通信系统的可靠性和频谱效率。本文将信源-信道联合编码(JSCC)和HARQ进行联合优化设计,并提出了基于矩阵扩展(ME)的信源-信道联合编码HARQ方案。每次传输时,ME-JSCC-HARQ方案都在前一次传输的极化编码矩阵的基础上扩展任意长度,并将该次传输的比特放置在扩展位上。由于极化编码矩阵的下三角结构,在联合编码过程中每次传输的比特都不会影响到信源比特和之前传输的编码比特。为了提高ME-JSCC-HARQ方案的译码可靠性,要选取扩展后的长极化码的最可靠的比特子信道作为信息比特子信道。该方案可以将信源信息与多次传输的信道信息进行联合设计,从而获得额外的联合编码增益。仿真结果表明,与分离式的基于信源极化编码和具有重传的信道极化编码方案相比,ME-JSCC-HARQ方案可以获得显著的性能增益。本文对极化编码理论进行研究,并深入研究极化码的结构,提出矩阵扩展框架,并结合广义极化变换理论,将极化编码和信号传输技术进行联合设计。在矩阵扩展框架下,研究了极化编码HARQ和信源-信道联合编码系统,并进一步将信源-信道联合编码和HARQ进行联合优化设计。上述研究内容完善了极化传输理论,提升了信号传输的可靠性、频谱效率和时延等,对无线通信系统空口技术的优化起指导作用。更多还原

【Abstract】 Polar codes,proposed by Professor Arikan,are a class of channel coding that have been rigorously proven to achieve the Shannon capacity,with their foundation rooted in the theory of channel polarization.Owing to their excellent error-correcting performance under finite blocklength,polar codes have been adopted in the 5G NR standard as the coding scheme for control channels in enhanced mobile broadband(eMBB)scenarios,making them of significant practical and academic interest.Despite their commercialization in 5G systems,the extension of polar codes to future communication systems,such as 6G,still faces multiple challenges.The concept of channel polarization represents a revolutionary breakthrough in coding theory.Moreover,it reveals a broader phenomenon—namely,the unequal reliability of data transmission that is widespread in communication systems—which can be interpreted as a generalized polarization effect.Joint optimization of polar coding and signal transmission technologies,guided by theoretical performance analysis,remains an area with substantial research potential.Motivated by this,this dissertation investigates polar coding theory starting from the generalized polarization phenomenon commonly observed in wireless communication systems and proposes a matrix extension(ME)framework.Based on this framework,a joint design of polar coding and transmission techniques is developed,resulting in a new polar-coded transmission theory and method.This work provides a solid theoretical and methodological foundation for the application of polar codes in next-generation mobile communication systems.Specifically,the main contributions of this dissertation are as follows:1)We investigate and design polar-coded hybrid automatic repeat request(HARQ)under high-order modulation.By integrating channel polarization principles into HARQ and coded modulation,a matrix extension(ME)scheme is proposed as a framework for polar-coded HARQ in bit-interleaved polar coded modulation(BIPCM).The ME-BIPCM scheme combines multiple independent polar subcodes into longer polar codes via matrix extension,allowing arbitrary subcode lengths.The ME-BIPCM process involves three steps:polar subcodes.matrix extension,and modulation polarization.The ME-HARQ scheme further extends ME-BIPCM by aggregating multiple transmissions into longer polar codes through four steps:polar subcodes,matrix extension(modulation sub-blocks),matrix extension(transmission blocks),and modulation polarization.For nonuniform underlying channels(e.g.,reliability disparities caused by highorder modulation),fixed sequences(e.g.,the polarization weight(PW)sequence or Polar sequence in the 5G standard)fail to construct optimal polar codes.The ME scheme addresses this issue by partitioning the underlying channels into different blocks according to their reliabilities,ensuring that the underlying channels for each polar subcode are of uniform reliability.Leveraging this property of the ME scheme,this dissertation further proposes a rate allocation(RA)method to investigate fast construction of the ME scheme.In the limit of infinite block length,the RA-constructed ME scheme can be proven to achieve the channel capacity.Simulation results indicate that,compared with GA-based constructions,the RA-based ME scheme achieves nearly identical performance with significantly reduced complexity and exhibits strong robustness under various parameter settings.Moreover,compared with the LDPC-coded modulation scheme in the 5G standard,the proposed scheme consistently achieves stable performance gains.2)This dissertation further investigates the theory of joint sourcechannel coding(JSCC)and proposes an ME-based JSCC scheme.Under the matrix extension framework,source polar coding(SPC)and channel polar coding are jointly designed.SPC can be implemented in both lossless and lossy manners,and we design ME-JSCC schemes based on both lossless SPC and lossy SPC.Under favorable channel conditions,lossless SPC should be adopted;however,under poor channel conditions,it becomes challenging for the receiver to recover the source without distortion,and lossy SPC should be employed.The ME-JSCC scheme leverages the fact that the polar coding matrix is lower triangular;by extending this matrix,a larger joint polar coding matrix is formed,resulting in a longer polar code.This approach enhances the coupling between source and channel,thereby achieving stronger joint source-channel polarization effects.Simulation results show that the ME-JSCC scheme employing lossless SPC outperforms both the DP-LDPC scheme and the double polar codes scheme under the J-SCL decoder,and it nearly attains the finite block-length performance limits of lossless JSCC.Under low signal-to-noise ratio conditions,the proposed ME-JSCC scheme with lossy SPC achieves further performance improvements compared to the ME-JSCC scheme with lossless SPC.Moreover,the compression rate obtained by the proposed adaptive lossy source compression rate method is almost identical to that achieved under the optimal compression rate determined via exhaustive search for the ME-JSCC scheme with lossy SPC,thereby validating the effectiveness of the proposed adaptive lossy source compression method.3)To further enhance the reliability and spectral efficiency of communication systems,this dissertation proposes a joint design that integrates JSCC with HARQ,introducing an matrix extension-based joint sourcechannel coding HARQ.For each transmission,the ME-JSCC-HARQ scheme extends polar coding matrix of the previous transmission by an arbitrary length and maps the bits of current transmission into the extended positions.Owing to the lower triangular structure of the polar coding matrix,the bits of each transmission do not affect the source bits or the coded bits from previous transmissions during joint encoding.To improve the decoding reliability of the ME-JSCC-HARQ scheme,the most reliable bit subchannels in the extended long polar code are selected as the information bit subchannels.This scheme jointly designs the source information and channel information over multiple transmissions to achieve additional joint coding gains.Simulation results demonstrate that,compared with separate scheme that employ source polar coding and channel polar coding with retransmission,the proposed ME-JSCC-HARQ scheme achieves significant performance gains.In summary,this dissertation explores polar coding theory and delves deeply into the structure of polar codes,proposing a matrix extension framework and,in conjunction with the theory of generalized polarization transforms,presents the joint design of polar coding and signal transmission techniques.Under the matrix extension framework,the dissertation investigates both polar-coded HARQ and joint source-channel coding systems,and further proposes a joint optimization design for JSCC and HARQ.These studies contribute to the advancement of polarization transmission theory,enhancing the reliability,spectral efficiency,and latency of signal transmission,and provide valuable guidance for the optimization of air interface technologies in wireless communication systems.更多还原